Distributed finite-time leaderless consensus control for double-integrator multi-agent systems with external disturbances

We study the finite-time consensus control of double-integrator multi-agent systems with external bounded disturbances under the fixed leaderless network communication topology. Based on the relative position and the relative velocity information, a novel finite-time consensus protocol is constructed. By using the Lyapnuov finite-time theory, it is shown that the proposed protocol can coordinate the states of agents to guarantee the finite-time consensus under an undirected connected topology. And then we extend the results onto the strongly connected directed communication topology. Importantly, the finite convergence time of the leaderless systems is explicitly presented. Finally, the effectiveness of the results is illustrated by numerical simulation.